1. Multiplication of Exponents Module 6, Lesson 2 Online Algebra VHS@PWCS

2. Review of Exponents Write the following expressions without using exponents. c5c5 c x c x c x c x c r4r4 r x r x r x r g8g8 g x g x g x g x g x g x g x g

3. Write the following without using exponents. What do you think that expression would be if we wrote it using exponents? We have a total of 7 x’s, of our expression would be x 7

4. Try some more. Write each expression out without using exponents. Then rewrite it using just one base with exponents. t 3 (t 6 ) (t)(t)(t) x (t)(t)(t)(t)(t)(t) t 9 52545254 (5 x 5)(5 x 5 x 5 x 5) 5 6 r(r 4 )(r 3 ) (r) x (r x r x r x r) x (r x r x r) r 8 Do you notice anything? When you multiply powers with the SAME base all you do is add the exponents!

5. Simplify each expression Use only positive exponents. 1. f 2 (f 3 ) 2. y(y 8 )(y 3 ) 3. r 5 (t 4 ) 4. g -5 (g 3 ) If a base has no exponent. It is always 1. If the bases are not the same the expression can not be simplified! -5 + 3 = -2, to make a negative exponent positive, you must change it from the top of the fraction to the bottom or vice versa. f5f5 y 12 r5t4r5t4

6. Try these! Simplify each expression use only positive exponents. 1. 3d 2 (-4d 3 ) -12d 5 2. a 2 (b 3 )(a 2 ) a4b3a4b3 3. (-2j -2 )(-3i 2 j -2 )(-5j -3 )

7. Multiplying Powers When multiplying powers with the same base: Add the exponents! You can regroup so that like variables are together and constants are together.